Impact of a Porosity-Dependent Retention Function on Simulations of Porous Flow

Abstract

Numerical models of flow in unsaturated porous media employ a range of functions to account for capillary effects. In general, these retention functions are assigned at the beginning of the simulation and calculate capillary pressure based on saturation. However, many porous systems involve changes in porosity wherein the retention function should change during the simulation. Model runs which neglect these changes may produce unphysical results such as retention of liquid water in air-filled void spaces. We present a conceptually and numerically simple function that recalculates the retention function at each timestep based on the updated porosity. The new retention function updates the maximum capillary pressure, residual saturation, and maximum saturation prior to applying the saturation fit. We compare results from a fixed (saturation-only) function and the new porosity-dependent retention function through a set of two numerical Gedankenexperiments in salt. The new retention function corrects unphysical model behaviors and causes dramatic changes in simulation behavior relative to the fixed (saturation-only) function, especially when applied to systems dominated by capillary effects. These changes result in large differences in simulated porosity, saturation, and volumetric water content. Water content results obtained using the porosity-dependent retention function are inverted compared to those obtained from saturation-only functions, with high-porosity nodes changing from very wet when using the saturation-only retention function to very dry when using the porosity-dependent retention function. These test cases suggest that dynamic retention functions in changing-porosity systems are important considerations to ensure sensible simulation results.